As a passenger, when I look out of the window, I can see the wings shaking. What would another plane (not in turbulence) see if they were observing the same plane (in turbulence)?
- The wings are flexing because there is a change in lift.
- The wings are more aerodynamic than the body of the aircraft. I.e. the wings are more "responsive", they respond to changed aerodynamic forces more rapidly.
- As a result of the change in lift in the wings, the body (being connected to the wings) follow the change.
Therefore, to an observer who is immune to turbulence, the wings would flex first, followed by the aircraft as a whole. If the turbulence is causing the wings to flex up and down repeatedly (e.g. imagine sine wave), the body of the aircraft can be observed lagging behind the wings and smaller in amplitude.
The wings act as a structural dampener to disturbances such as turbulence, similar to the suspension on a car. As they flex, they absorb the sudden energy changes. The aerodynamic forces also take time to accelerate the large mass of the airplane. Because of these effects, most of turbulence will be too small to see from an outside observer's point of view.
However, in addition to the wing flexing, the aircraft will also roll, pitch, and yaw in response to the turbulence. The pilots or the autopilot, as well as the natural stability tendencies of the aircraft, will help the aircraft return to its previous state.
Here is a video recorded from the X-Plane flight simulator program of a 737 in turbulence. The wing flex and change in flight attitude can be seen.
Let's suppose you stand on an unstable bar stool. It shakes a little when you move, but you feel a lot of movement. An observer standing close by will see the stool and you shake a little bit (a few inches at most). If that observer moves a 100 feet away, he might not notice the shaking at all.
When the airplane you are on is in turbulence1, you will feel a lot of shaking. The airplane is shaking, but to an outside observer which is close, it will feel as much as you feel it. Again, if the observer is moved a mile away, the shaking will not appear as significant as your experience.
1 Minor turbulence. In case of severe turbulence, it will be more evident to an observer.